This a computational challenge, to find an efficient algorithm to discover a quadruple $(n,n+1,n+2,n+3)$ with the same sum of prime factors as described in the MO question, "Ruth-Aaron triples, etc." E.g., $$417,164 = 2^2 \cdot 11 \cdot 19 \cdot 499 \;;\; 2+2+11+19+499 = 533 \;.$$ The sum can be computed by multiplying the exponent in the prime factorization times the base prime:
SumFact[n_] := Apply[Plus, Map[#[] #[] &, FactorInteger[n]]];
Apparently no such quadruple is known, and I've checked through $n=10^7$, and am now trying to reach $10^8$ in the next day or so. But my computation is naive in terms of efficient computation. Also, I do not have easy access to significant computational resources.
As far as I can make out, there is no known such quadruple.